Controversial radio host Alex Jones has been sued by the parents of several Sandy Hook shooting victims over his claims that the 2012 massacre was staged.

Three parents who lost children in the mass shooting sued the InfoWars host for defamation, claiming his comments on the incident caused them mental stress and anguish, as well as damage to their reputations.

“Our clients have been tormented for five years by Mr Jones’ ghoulish accusations that they are actors who faked their children’s deaths as part of a fraud on the American people,” said attorney Mr Bankston, who has also sued Mr Jones for falsely identifying the gunman in a school shooting in Parkland, Florida.

He added: “Enough is enough.”

Mr Jones and InfoWars did not respond to a request for comment.

Mr Jones – a celebrity in far-right media circles for his bombastic, often unverified reporting – has suggested since 2013 that the shooting at Sandy Hook Elementary may have been faked by the government and covered up with the help of the victims’ families.

In 2014, he claimed that Veronique De La Rosa, one of the plaintiffs in the lawsuit, had participated in a staged interview with CNN’s Anderson Cooper about the death of her son. He claimed the interview was conducted in a studio, in front of a “blue screen,” and doctored to look as if it was shot on location.

The next year, he circulated a conspiracy theory about Ms De La Rosa’s son, whose photo was seen at a vigil for victims of a school attack in Pakistan. The photo was part of a tribute to children lost in school attacks around the world, according to the lawsuit.

Mr Jones repeated his claims about Ms De La Rosa last year, in a broadcast titled “Sandy Hook Vampires Exposed.” He claimed her interview must have been staged because of a moment in which Mr Cooper’s nose seems to disappear. The moment is in fact the result of motion compensation video compression, and does not occur in high-quality videos of the interview.

That same year, Mr Jones spoke out about another of the plaintiffs, Neil Heslin, who lost his son in the shooting. Mr Heslin had told NBC’s Megyn Kelly about how he “held [his] son with a bullet hole through his head”.

Mr Jones responded by airing a segment in which a reporter claimed that this was not possible, because coroners had said victims were originally identified by their photos, not their bodies.

“Will there be a clarification from Heslin or Megyn Kelly?” the reporter, Owen Shroyer, asked. “I wouldn’t hold your breath. So now they’re fuelling the conspiracy theory claims.”

News reports from the time show the victims’ bodies were ultimately released to funeral homes.

Mr Bankston filed the suits on behalf of Mr Heslin, Ms De La Rosa, and her ex-husband Leonard Pozner in Travis County District Court in Texas on Monday. He said the families had been deeply hurt by Mr Jones’s comments, which he called “the most disgusting act of defamation in the history of American media”.

“In all our years of helping families who have lost loved ones under horrific circumstances, we have never seen victims subjected to this kind of malicious cruelty,” he said. “Their pain is unfathomable.”